Chapter 16 Section 9: Optics and Mechanics in the Mojing

"Mo Jing" was originally four chapters in the book "Mozi", "Jing Shang", "Jing Xia", "Jing Shuo Shang", and "Jing Shuo Xia". through".There are still disputes about the author of the "Mojing". It is said; some people think that the four articles are all works of Mohists in the late Warring States period.But apart from its author, in terms of content alone, historians believe that it is an important scientific classic in the pre-Qin period.Its scientific content is very rich, in addition to the geometry mentioned above, the prominent ones are optics and mechanics.

The earliest small hole imaging experiment in my country is recorded in the "Mojing": a small hole is opened on a wall facing the sun in a small house, and a person stands outside the house facing the small hole. An upside down figure will appear.In this regard, the "Mojing" explains that this is because the light travels in a straight line like an arrow when passing through the small hole. The head of the person blocks the light from above, so the shadow is below, while the feet of the person Part of the light from below is covered, so the shadow is on the top, thus forming an inverted image.This not only clearly expounds the principle of linear propagation of light, but also scientifically explains the principle of pinhole imaging.

As for the imaging problems of concave mirrors, convex mirrors, and plane mirrors, the "Mojing" has made more systematic research and discussions.People now know that a convex lens can focus on the sun to make fire.In the pre-Qin period, there were no glass lenses in my country, but there were a large number of bronze mirrors.At that time, people had discovered that the concave mirror could focus on making fire, so it was also called Yangsui, and using it to make fire was an important method of artificially making fire. The "Mojing" made a series of investigations on the imaging principle of concave mirrors, pointing out that outside the center of the concave mirror, the image formed by the object is inverted and smaller than the original object; within the center of the sphere, the image is upright , larger than the original. The "Mojing" also pointed out that the images formed by convex mirrors are all upright and smaller than the original object; while the images formed by flat mirrors are as large as the original object, but the left and right sides are inverted.Comparing these expositions in Mojing with modern geometric optics, except that it has not been able to distinguish the focal point from the center of the sphere, the other contents are consistent.

There are also incisive discussions in the "Mojing" about the shadow of moving objects.It points out that the shadow of a moving object does not move with the object. This is because the shadow that appears after the object moves is newly formed, while the original shadow has disappeared after the object moves. It seems that the shadow is also moving, but it is just old and new. The shadows are constantly replacing each other. The "Mojing" also examines the issue of umbra and penumbra, and has a scientific explanation.It is remarkable to have such an achievement more than 2,000 years ago.

In terms of mechanics, the "Mojing" gives the definition of force: "force, the reason why punishment (ancient Tong Xing) is vigorous", means that force is the means of the human body to move objects, such as from bottom to top. Lifting heavy objects is the effect of force.It derives the principle of leverage from the balance of the weighing apparatus, that is, force × force arm = heavy × heavy arm.For mechanical problems such as motion, rest, buoyancy, center of gravity, and inclined planes, there are also quite incisive descriptions in the "Mojing", so I won't list them here.